Development of mechanics of a rocking problem

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In summary, the conversation discusses the mechanics of a problem involving an inverted glass and a mass on top of it. The goal is to find the vertical force or acceleration of the mass when the glass is released and comes into full contact with the table. The glass is assumed to be rigid and with insignificant mass, and the contact between the glass base and table is represented by a linear spring with stiffness K. The conversation also mentions finding the relationship between the lateral velocity and vertical acceleration of the mass.
  • #1
Hector92
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Hi
I want to develop mechanics of a problem which is as follows.

Suppose there is an inverted glass (cylinder) lying on a table. Now suppose there is a mass (or coin) on the top of glass. If we provide an initial rotation to the glass such that only one corner of glass is in contact with table (no overturning) and then release it. Now when the glass will come in full contact with table then the coin will lift vertically. I want to find out the vertical force (acceleration) acting on the top mass or coin using mechanics.

(Suppose glass or cylinder is rigid and with insignificant mass. Only mass acting is the top mass (m). No shear slip. Contact of glass base and table can be represented by a linear spring with stiffness K).

Thanks and Regards
 
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  • #2
I have found the lateral velocity and vertical acceleration of the top mass and are directly proportional to each other. I want to find out the relationship between two
 

1. What is the purpose of studying the development of mechanics of a rocking problem?

The purpose of studying the development of mechanics of a rocking problem is to understand the underlying principles and factors that contribute to the phenomenon of a rocking motion. This knowledge can then be applied to various fields such as engineering, physics, and mathematics to design more stable structures and improve their performance.

2. What are the key factors that affect the mechanics of a rocking problem?

The key factors that affect the mechanics of a rocking problem include the geometry and weight distribution of the object, the surface on which it is rocking, and external forces such as wind or vibrations. These factors can influence the stability and motion of the object and must be carefully considered in its design and analysis.

3. How does the center of mass play a role in the mechanics of a rocking problem?

The center of mass is a crucial factor in the mechanics of a rocking problem as it determines the point around which the object will rotate or rock. A higher center of mass may lead to a less stable rocking motion, while a lower center of mass can improve stability. It is important to carefully consider the center of mass in the design of objects to minimize the risk of rocking.

4. What are some real-world applications of the study of mechanics of a rocking problem?

The study of mechanics of a rocking problem has various real-world applications. It is used in the design of structures such as bridges, buildings, and offshore platforms to ensure their stability and safety against rocking motions caused by external forces. It is also applied in the design of furniture, vehicles, and other objects to improve their stability and performance.

5. How can the study of mechanics of a rocking problem benefit society?

By understanding the mechanics of a rocking problem, we can design more stable and safer structures, furniture, and objects. This can prevent accidents and improve the overall safety and reliability of various industries. Additionally, the study of mechanics of a rocking problem can also lead to advancements in other fields such as robotics and biomechanics, enhancing our understanding and ability to control motion in various systems.

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